Metric spaces underlying complex networks provide a fundamental explanation of their observed topologies [1]}, [2]}. In the class of models used here [3]}, every node is characterized by a hidden degree and an angular coordinate \((\kappa _i,\theta _i)\)  abstracting the popularity and similarity attributes of nodes. The \(N\)  nodes of the network are distributed at random in the similarity space, which is taken to be a circle of radius \(R_{\mathbb {S}^1}=N/2\pi ,\)  so that the density of nodes equals 1. To generate networks based in such hidden metric space we distribute nodes on the circle using a uniform distribution \(\mathcal {U}_{[0,2\pi )}\)  and draw their \(\kappa \)  coordinates from a power-law distribution \(\rho (\kappa )\sim \kappa ^{-\gamma }\)  in order to generate scale-free networks. Then, every pair of nodes is connected with probability
\( p_{ij} = \frac{1}{1 + \left( \frac{\Delta \theta _{ij}R_{\mathbb {S}^1}}{\mu \kappa _i \kappa _j} \right)^\beta },\) 
